A125762 Number of planar Langford sequences.

0, 0, 1, 0, 0, 0, 0, 4, 0, 0, 16, 40, 0, 0, 194, 274, 0, 0, 2384, 4719, 0, 0, 31856, 62124, 0, 0, 426502, 817717, 0, 0, 5724640, 10838471, 0, 0, 75178742, 142349245, 0, 0, 977964587, 1850941916, 0, 0

Offset: 1

Author

Don Knuth, Feb 03 2007

Keywords

• nonn
• more

Comments

Enumerates the Langford sequences (counted by A014552) that have the additional property that we can draw noncrossing lines to connect the two 1s, the two 2s, ..., the two ns. For example, the four solutions for n=8 are 8642752468357131, 8613175368425724, 5286235743681417, 7528623574368141.

References

• D. E. Knuth, TAOCP, Vol. 4, in preparation.

Links

• John E. Miller, Langford's Problem
• Edward Moody, Java program for enumerating planar Langford sequences
• Zan Pan, Conjectures on the number of Langford sequences, (2021).

Crossrefs

Cf. A014552, A059106.

Extensions

a(31) from Rory Molinari, Feb 21 2018

a(32)-a(34) from Rory Molinari, Mar 10 2018

a(35) from Rory Molinari, May 02 2018

a(36)-a(42) from Edward Moody, Apr 02 2019